Theorem cgsexg 3142

Description: Implicit substitution inference for general classes. (Contributed by NM, 26-Aug-2007.)

Hypotheses

Ref	Expression
cgsexg.1
cgsexg.2

Assertion

Ref	Expression
cgsexg

Distinct variable groups:   ,   ,

Proof of Theorem cgsexg

Step	Hyp	Ref	Expression
1		cgsexg.2	. . . 4
2	1	biimpa 484	. . 3
3	2	exlimiv 1722	. 2
4		elisset 3120	. . . 4
5		cgsexg.1	. . . . 5
6	5	eximi 1656	. . . 4
7	4, 6	syl 16	. . 3
8	1	biimprcd 225	. . . . 5
9	8	ancld 553	. . . 4
10	9	eximdv 1710	. . 3
11	7, 10	syl5com 30	. 2
12	3, 11	impbid2 204	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111